(x-3)(3x+5)+4x(2x+1)=7x^2+12x-20

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Solution for (x-3)(3x+5)+4x(2x+1)=7x^2+12x-20 equation: 


Simplifying
(x + -3)(3x + 5) + 4x(2x + 1) = 7x2 + 12x + -20

Reorder the terms:
(-3 + x)(3x + 5) + 4x(2x + 1) = 7x2 + 12x + -20

Reorder the terms:
(-3 + x)(5 + 3x) + 4x(2x + 1) = 7x2 + 12x + -20

Multiply (-3 + x) * (5 + 3x)
(-3(5 + 3x) + x(5 + 3x)) + 4x(2x + 1) = 7x2 + 12x + -20
((5 * -3 + 3x * -3) + x(5 + 3x)) + 4x(2x + 1) = 7x2 + 12x + -20
((-15 + -9x) + x(5 + 3x)) + 4x(2x + 1) = 7x2 + 12x + -20
(-15 + -9x + (5 * x + 3x * x)) + 4x(2x + 1) = 7x2 + 12x + -20
(-15 + -9x + (5x + 3x2)) + 4x(2x + 1) = 7x2 + 12x + -20

Combine like terms: -9x + 5x = -4x
(-15 + -4x + 3x2) + 4x(2x + 1) = 7x2 + 12x + -20

Reorder the terms:
-15 + -4x + 3x2 + 4x(1 + 2x) = 7x2 + 12x + -20
-15 + -4x + 3x2 + (1 * 4x + 2x * 4x) = 7x2 + 12x + -20
-15 + -4x + 3x2 + (4x + 8x2) = 7x2 + 12x + -20

Reorder the terms:
-15 + -4x + 4x + 3x2 + 8x2 = 7x2 + 12x + -20

Combine like terms: -4x + 4x = 0
-15 + 0 + 3x2 + 8x2 = 7x2 + 12x + -20
-15 + 3x2 + 8x2 = 7x2 + 12x + -20

Combine like terms: 3x2 + 8x2 = 11x2
-15 + 11x2 = 7x2 + 12x + -20

Reorder the terms:
-15 + 11x2 = -20 + 12x + 7x2

Solving
-15 + 11x2 = -20 + 12x + 7x2

Solving for variable 'x'.

Reorder the terms:
-15 + 20 + -12x + 11x2 + -7x2 = -20 + 12x + 7x2 + 20 + -12x + -7x2

Combine like terms: -15 + 20 = 5
5 + -12x + 11x2 + -7x2 = -20 + 12x + 7x2 + 20 + -12x + -7x2

Combine like terms: 11x2 + -7x2 = 4x2
5 + -12x + 4x2 = -20 + 12x + 7x2 + 20 + -12x + -7x2

Reorder the terms:
5 + -12x + 4x2 = -20 + 20 + 12x + -12x + 7x2 + -7x2

Combine like terms: -20 + 20 = 0
5 + -12x + 4x2 = 0 + 12x + -12x + 7x2 + -7x2
5 + -12x + 4x2 = 12x + -12x + 7x2 + -7x2

Combine like terms: 12x + -12x = 0
5 + -12x + 4x2 = 0 + 7x2 + -7x2
5 + -12x + 4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
5 + -12x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.5, 2.5}

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